To study the anisotropy in the CuO_2 planes, the in-plane resistivity ρ has been measured on 60 K YBa_2Cu_3O_<7-δ> (YBCO) single crystal as a function of the angle θ between the directions of a magnetic field H and of the b axis under magnetic fields precisely parallel to the CuO_2 planes. Angular dependence of the resistivity ρ(θ) is mainly described by the fourfold symmetry, and a dip structure appears in ρ(θ) when the magnetic field is applied parallel to the a and b axes. The fourfold symmetry of the in-plane anisotropy of the resistivity is first observed in YBCO system. It is shown that the obtained results have a very close relation to the anisotropy which comes from the superconducting energy gap of the d-wave pairing with d_<x2-y2> symmetry and the effect of the directional vortex pinning.